Question: Solve for $x$ and $y$ using elimination. ${-5x-y = -41}$ ${-6x+y = -36}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-11x = -77$ $\dfrac{-11x}{{-11}} = \dfrac{-77}{{-11}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-5x-y = -41}\thinspace$ to find $y$ ${-5}{(7)}{ - y = -41}$ $-35-y = -41$ $-35{+35} - y = -41{+35}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {-6x+y = -36}\thinspace$ and get the same answer for $y$ : ${-6}{(7)}{ + y = -36}$ ${y = 6}$